Buda Royal Palace (Kiralyi Palota)
The grandiose pile of the Királyi Palota (the Royal Palace) is the Phoenix of Budapest - it's been burnt to the ground and rebuilt countless times, and was almost gone in WWII. But these days, looking at the magnificent stone edifice and haughty dome, it's hard to believe it was ever in jeopardy.
Three of Budapest's premier museums are housed in the Royal Palace. The Hungarian National Gallery has rooms of paintings by Hungarian artists ranging from medieval times through to the 20th century. The Budapest History Museum is famed for its Gothic rooms and statues, unearthed in the 1960s during a renovation of the castle. The National Library holds a collection of all Hungarian works.
The gardens offer sweeping views down Castle Hill, and various statues. Follow the groups of tourists to the Matthias Well, a Romantic extravaganza of a fountain with the figure of the young King Matthias as a hunter with his stag, and his beautiful beloved with her doe.
Entrance to the palace is free - this will get you a gaze at its splendor, a stroll around the grounds, some wild statues and those magnificent views. The museums each have separate admission fees.
The best way up Buda Hill is to take the funicular, which will allow you a lazy look at the vistas. You can also walk up, but be warned - the hill is steep!